Title :

Adaptive directional estimator of the density in R^d for independent and mixing sequences

Author(s) :

Ammous, Sinda [Auteur]
Mathématiques Appliquées Paris 5 [MAP5 - UMR 8145]
Dedecker, Jérôme [Auteur]
Mathématiques Appliquées Paris 5 [MAP5 - UMR 8145]
Duval, Céline [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

Adaptive procedure
Anisotropy
Density estimation
Dependence
Stationary sequences
Fourier transform

HAL domain(s) :

Mathématiques [math]/Mathématiques générales [math.GM]

English abstract : [en]

A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the ...
Show more >A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the smoothness of the density; it is directly adaptive. We establish oracle inequalities valid for independent, α-mixing and τ-mixing sequences, which allows us to derive optimal convergence rates, up to a logarithmic loss. On general anisotropic Sobolev classes, the estimator adapts to the regularity of the unknown density but also achieves directional adaptivity. In particular, if A is an invertible matrix, if the observations are drawn from X ∈ R^d , d ≥ 1, it achieves the rate implied by the regularity of AX, which may be more regular than X. The estimator is easy to implement and numerically efficient. It depends on the calibration of a parameter for which we propose an innovative numerical selection procedure, using the Euler characteristic of the thresholded areas.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL